<!DOCTYPE html>
<html lang="zh-CN">
<head>
  <meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=2">
<meta name="theme-color" content="#222">
<meta name="generator" content="Hexo 5.2.0">
  <link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon-next.png">
  <link rel="icon" type="image/png" sizes="32x32" href="/images/favicon-32x32-next.png">
  <link rel="icon" type="image/png" sizes="16x16" href="/images/favicon-16x16-next.png">
  <link rel="mask-icon" href="/images/logo.svg" color="#222">

<link rel="stylesheet" href="/css/main.css">


<link rel="stylesheet" href="/lib/font-awesome/css/all.min.css">

<script id="hexo-configurations">
    var NexT = window.NexT || {};
    var CONFIG = {"hostname":"hanayabuki.gitee.io","root":"/","scheme":"Gemini","version":"7.8.0","exturl":false,"sidebar":{"position":"left","width":240,"display":"always","padding":18,"offset":12,"onmobile":false},"copycode":{"enable":true,"show_result":false,"style":null},"back2top":{"enable":true,"sidebar":false,"scrollpercent":false},"bookmark":{"enable":false,"color":"#222","save":"auto"},"fancybox":false,"mediumzoom":false,"lazyload":true,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"algolia":{"hits":{"per_page":10},"labels":{"input_placeholder":"Search for Posts","hits_empty":"We didn't find any results for the search: ${query}","hits_stats":"${hits} results found in ${time} ms"}},"localsearch":{"enable":false,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false},"motion":{"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"slideDownIn","post_body":"slideDownIn","coll_header":"slideLeftIn","sidebar":"slideUpIn"}}};
  </script>

  <meta name="description" content="排序算法总结(二) - 摘要 ♈ 排序算法总览 ♉ 分析O(nlogn)的排序算法 ♊ 代码实现 ♋ 实用角度分析">
<meta property="og:type" content="article">
<meta property="og:title" content="排序算法总结(二)">
<meta property="og:url" content="http://hanayabuki.gitee.io/2020/11/29/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E7%BB%93-%E4%BA%8C/index.html">
<meta property="og:site_name" content="花枝丸🍥的博客">
<meta property="og:description" content="排序算法总结(二) - 摘要 ♈ 排序算法总览 ♉ 分析O(nlogn)的排序算法 ♊ 代码实现 ♋ 实用角度分析">
<meta property="og:locale" content="zh_CN">
<meta property="og:image" content="https://imgconvert.csdnimg.cn/aHR0cHM6Ly9pbWFnZXMyMDE3LmNuYmxvZ3MuY29tL2Jsb2cvODQ5NTg5LzIwMTcxMC84NDk1ODktMjAxNzEwMTUyMzMwNDMxNjgtMTg2NzgxNzg2OS5wbmc?x-oss-process=image/format,png">
<meta property="article:published_time" content="2020-11-29T13:52:47.000Z">
<meta property="article:modified_time" content="2020-12-02T12:19:42.594Z">
<meta property="article:author" content="Hanamaru🍥Yabuki">
<meta property="article:tag" content="排序算法">
<meta property="article:tag" content="Java">
<meta name="twitter:card" content="summary">
<meta name="twitter:image" content="https://imgconvert.csdnimg.cn/aHR0cHM6Ly9pbWFnZXMyMDE3LmNuYmxvZ3MuY29tL2Jsb2cvODQ5NTg5LzIwMTcxMC84NDk1ODktMjAxNzEwMTUyMzMwNDMxNjgtMTg2NzgxNzg2OS5wbmc?x-oss-process=image/format,png">

<link rel="canonical" href="http://hanayabuki.gitee.io/2020/11/29/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E7%BB%93-%E4%BA%8C/">


<script id="page-configurations">
  // https://hexo.io/docs/variables.html
  CONFIG.page = {
    sidebar: "",
    isHome : false,
    isPost : true,
    lang   : 'zh-CN'
  };
</script>

  <title>排序算法总结(二) | 花枝丸🍥的博客</title>
  






  <noscript>
  <style>
  .use-motion .brand,
  .use-motion .menu-item,
  .sidebar-inner,
  .use-motion .post-block,
  .use-motion .pagination,
  .use-motion .comments,
  .use-motion .post-header,
  .use-motion .post-body,
  .use-motion .collection-header { opacity: initial; }

  .use-motion .site-title,
  .use-motion .site-subtitle {
    opacity: initial;
    top: initial;
  }

  .use-motion .logo-line-before i { left: initial; }
  .use-motion .logo-line-after i { right: initial; }
  </style>
</noscript>

</head>

<body itemscope itemtype="http://schema.org/WebPage">
  <div class="container use-motion">
    <div class="headband"></div>

    <header class="header" itemscope itemtype="http://schema.org/WPHeader">
      <div class="header-inner"><div class="site-brand-container">
  <div class="site-nav-toggle">
    <div class="toggle" aria-label="切换导航栏">
      <span class="toggle-line toggle-line-first"></span>
      <span class="toggle-line toggle-line-middle"></span>
      <span class="toggle-line toggle-line-last"></span>
    </div>
  </div>

  <div class="site-meta">

    <a href="/" class="brand" rel="start">
      <span class="logo-line-before"><i></i></span>
      <h1 class="site-title">花枝丸🍥的博客</h1>
      <span class="logo-line-after"><i></i></span>
    </a>
      <p class="site-subtitle" itemprop="description">记录自己作为CS学生的点滴</p>
  </div>

  <div class="site-nav-right">
    <div class="toggle popup-trigger">
    </div>
  </div>
</div>




<nav class="site-nav">
  <ul id="menu" class="main-menu menu">
        <li class="menu-item menu-item-home">

    <a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a>

  </li>
        <li class="menu-item menu-item-about">

    <a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a>

  </li>
        <li class="menu-item menu-item-tags">

    <a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签<span class="badge">7</span></a>

  </li>
        <li class="menu-item menu-item-categories">

    <a href="/categories/" rel="section"><i class="fa fa-th fa-fw"></i>分类<span class="badge">5</span></a>

  </li>
        <li class="menu-item menu-item-archives">

    <a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档<span class="badge">13</span></a>

  </li>
  </ul>
</nav>




</div>
    </header>

    
  <div class="back-to-top">
    <i class="fa fa-arrow-up"></i>
    <span>0%</span>
  </div>
  <div class="reading-progress-bar"></div>

  <a href="https://github.com/HanaYabuki" class="github-corner" title="Follow me on GitHub" aria-label="Follow me on GitHub" rel="noopener" target="_blank"><svg width="80" height="80" viewBox="0 0 250 250" aria-hidden="true"><path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path><path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2" fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path><path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z" fill="currentColor" class="octo-body"></path></svg></a>


    <main class="main">
      <div class="main-inner">
        <div class="content-wrap">
          

          <div class="content post posts-expand">
            

    
  
  
  <article itemscope itemtype="http://schema.org/Article" class="post-block" lang="zh-CN">
    <link itemprop="mainEntityOfPage" href="http://hanayabuki.gitee.io/2020/11/29/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E7%BB%93-%E4%BA%8C/">

    <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
      <meta itemprop="image" content="/images/avatar.gif">
      <meta itemprop="name" content="Hanamaru🍥Yabuki">
      <meta itemprop="description" content="">
    </span>

    <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
      <meta itemprop="name" content="花枝丸🍥的博客">
    </span>
      <header class="post-header">
        <h1 class="post-title" itemprop="name headline">
          排序算法总结(二)
        </h1>

        <div class="post-meta">
            <span class="post-meta-item">
              <span class="post-meta-item-icon">
                <i class="far fa-calendar"></i>
              </span>
              <span class="post-meta-item-text">发表于</span>

              <time title="创建时间：2020-11-29 21:52:47" itemprop="dateCreated datePublished" datetime="2020-11-29T21:52:47+08:00">2020-11-29</time>
            </span>
              <span class="post-meta-item">
                <span class="post-meta-item-icon">
                  <i class="far fa-calendar-check"></i>
                </span>
                <span class="post-meta-item-text">更新于</span>
                <time title="修改时间：2020-12-02 20:19:42" itemprop="dateModified" datetime="2020-12-02T20:19:42+08:00">2020-12-02</time>
              </span>
            <span class="post-meta-item">
              <span class="post-meta-item-icon">
                <i class="far fa-folder"></i>
              </span>
              <span class="post-meta-item-text">分类于</span>
                <span itemprop="about" itemscope itemtype="http://schema.org/Thing">
                  <a href="/categories/%E7%AE%97%E6%B3%95/" itemprop="url" rel="index"><span itemprop="name">算法</span></a>
                </span>
            </span>

          

        </div>
      </header>

    
    
    
    <div class="post-body" itemprop="articleBody">

      
        <h2 id="排序算法总结-二-摘要"><a href="#排序算法总结-二-摘要" class="headerlink" title="排序算法总结(二) - 摘要"></a>排序算法总结(二) - 摘要</h2><ol>
<li>♈ 排序算法总览</li>
<li>♉ 分析O(nlogn)的排序算法</li>
<li>♊ 代码实现</li>
<li>♋ 实用角度分析</li>
</ol>
<a id="more"></a>

<h2 id="照例先来-排序算法总览"><a href="#照例先来-排序算法总览" class="headerlink" title="照例先来 排序算法总览"></a>照例先来 排序算法总览</h2><p><img data-src="https://imgconvert.csdnimg.cn/aHR0cHM6Ly9pbWFnZXMyMDE3LmNuYmxvZ3MuY29tL2Jsb2cvODQ5NTg5LzIwMTcxMC84NDk1ODktMjAxNzEwMTUyMzMwNDMxNjgtMTg2NzgxNzg2OS5wbmc?x-oss-process=image/format,png" alt="别人家里偷来的排序介绍表"></p>
<hr>
<p>本文详解 O(nlogn) 的几种排序算法, 代码实现以 Java 为例.</p>
<p>所有的排序均为对整型变量序列<code>int[]</code>排序, 结果均为升序. </p>
<h3 id="归并排序-MergeSort"><a href="#归并排序-MergeSort" class="headerlink" title="归并排序 MergeSort"></a>归并排序 MergeSort</h3><h4 id="原理"><a href="#原理" class="headerlink" title="原理"></a>原理</h4><p>归并排序是编程中递归思想的绝佳体现.</p>
<p>简单来讲, 归并排序采用分治思想</p>
<ol>
<li>将整个数组分成左右两个部分, 分别对左右两个部分排序</li>
<li>排序以后合并两个数组, 方法是 : 使用两个指针分别指向子序列开始, 一个指针指向待填充序列. 每步比较两指针的值大小, 小的一方填入带填充位置, 并指针后移, 随后待填充序列指针后移. 直到无法比较, 填充剩余序列. </li>
</ol>
<p>两步骤中, 第一步我们需要已经排好的两份序列, 而他们的排序方式就是这个方式本身. 这很好的体现了递归思想. </p>
<h4 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h4><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">MergeSort</span> </span>&#123;</span><br><span class="line">    <span class="comment">// 递归处理</span></span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sortRecursive</span><span class="params">(<span class="keyword">int</span>[] arr, <span class="keyword">int</span>[] res, <span class="keyword">int</span> start, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">if</span>(start &gt;= end) &#123; <span class="keyword">return</span>; &#125;</span><br><span class="line">        <span class="comment">// 计算长度, 计算中点</span></span><br><span class="line">        <span class="keyword">int</span> len = end - start, mid = (len/<span class="number">2</span>) + start;</span><br><span class="line">        <span class="comment">// 规定两次递归处理的指针</span></span><br><span class="line">        <span class="keyword">int</span> start1 = start, end1 = mid;</span><br><span class="line">        <span class="keyword">int</span> start2 = mid+<span class="number">1</span>, end2 = end;</span><br><span class="line">        <span class="comment">// 递归</span></span><br><span class="line">        sortRecursive(arr, res, start1, end1);</span><br><span class="line">        sortRecursive(arr, res, start2, end2);</span><br><span class="line">        <span class="comment">// 遍历处理当前层</span></span><br><span class="line">        <span class="keyword">int</span> k = start;</span><br><span class="line">        <span class="keyword">while</span> (start1 &lt;= end1 &amp;&amp; start2 &lt;= end2) &#123;</span><br><span class="line">            res[k++] = arr[start1] &lt; arr[start2] ? arr[start1++] : arr[start2++];</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// 某一侧处理完成, 顺延安置后续元素</span></span><br><span class="line">        <span class="keyword">while</span> (start1 &lt;= end1) &#123;</span><br><span class="line">            res[k++] = arr[start1++];</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">while</span> (start2 &lt;= end2) &#123;</span><br><span class="line">            res[k++] = arr[start2++];</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// 元素归回</span></span><br><span class="line">        <span class="keyword">for</span>(k = start; k &lt;= end; ++k) &#123;</span><br><span class="line">            arr[k] = res[k];</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 递归实现</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(<span class="keyword">int</span>[] arr)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> len = arr.length;</span><br><span class="line">        <span class="keyword">int</span>[] result = <span class="keyword">new</span> <span class="keyword">int</span>[len];</span><br><span class="line">        sortRecursive(arr, result, <span class="number">0</span>, len-<span class="number">1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="实用分析"><a href="#实用分析" class="headerlink" title="实用分析"></a>实用分析</h4><p>归并排序的比较都是根据相邻元素的, 相比快速排序来讲, 他是稳定排序.<br>弊端是必须引入额外空间, 而且在数据逐渐增多时, 元素的操作越来越频繁, 优势逐渐减弱.</p>
<hr>
<h3 id="希尔排序-ShellSort"><a href="#希尔排序-ShellSort" class="headerlink" title="希尔排序 ShellSort"></a>希尔排序 ShellSort</h3><h4 id="原理-1"><a href="#原理-1" class="headerlink" title="原理"></a>原理</h4><p>希尔排序原理基于插入排序. 由于插入排序对于较为有序的序列来说是高效的, 希尔排序正是利用了这一点来优化其本身的算法. </p>
<ol>
<li>取一个小于序列长度的整数 n , 作为当前步长. 把序列的元素分成 n 组, 所有互相之间距离为 n 的元素在这个组内. (即, 每隔n元素就抽出来放到同一组)</li>
<li>每组内进行插入排序</li>
<li>取一个更小的增量 n, 重复上述操作, 直到 n=1, 完成最后一次插入排序.</li>
</ol>
<h4 id="代码实现-1"><a href="#代码实现-1" class="headerlink" title="代码实现"></a>代码实现</h4><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">ShellSort</span> </span>&#123;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(<span class="keyword">int</span>[] arr)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> gap = <span class="number">1</span>, len = arr.length;</span><br><span class="line">        <span class="keyword">int</span> temp;</span><br><span class="line">        <span class="keyword">while</span> (gap &lt; len / <span class="number">3</span>) &#123;</span><br><span class="line">            gap = gap*<span class="number">3</span> + <span class="number">1</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// 递减步长</span></span><br><span class="line">        <span class="keyword">for</span> (; gap &gt; <span class="number">0</span>; gap /= <span class="number">3</span>) &#123;</span><br><span class="line">            <span class="comment">// 实现插入排序</span></span><br><span class="line">            <span class="keyword">for</span> (<span class="keyword">int</span> i = gap; i &lt; len; i++) &#123;</span><br><span class="line">                temp = arr[i];</span><br><span class="line">                <span class="keyword">int</span> j;</span><br><span class="line">                <span class="keyword">for</span> (j = i - gap; j &gt;= <span class="number">0</span> &amp;&amp; arr[j] &gt; temp; j -= gap) &#123;</span><br><span class="line">                    arr[j + gap] = arr[j];</span><br><span class="line">                &#125;</span><br><span class="line">                arr[j + gap] = temp;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h4 id="实用分析-1"><a href="#实用分析-1" class="headerlink" title="实用分析"></a>实用分析</h4><p>希尔排序算法的效率不是最高的, 但是他有很深刻的历史意义. 希尔排序从实践的角度, 验证了排序是可以被算法优化的. </p>
<p>现在基本上不再使用希尔排序, 其本身的思路也较为繁琐.</p>
<hr>
<h3 id="快速排序-QuickSort"><a href="#快速排序-QuickSort" class="headerlink" title="快速排序 QuickSort"></a>快速排序 QuickSort</h3><h4 id="原理-2"><a href="#原理-2" class="headerlink" title="原理"></a>原理</h4><p>快速排序是最普遍使用的排序方案. 很多语言内置的排序算法底层中所使用的(例如C++的<code>sort()</code>), 就是快速排序.</p>
<p>快速排序又叫 划分交换排序, 本质上也使用了分治思想. 但是, 他的思路更加难以理解, 需要详细阐述. </p>
<ol>
<li>在整个序列中, 选择末尾元素, 作为一个基准.</li>
<li>声明两个指针<code>p1</code>,<code>p2</code>, 依次 从左至右和从右至左 遍历整个序列. 当<code>p1</code>元素大于基准时停止之, 当<code>p2</code>元素小于基准时停止之. 此时, 交换<code>p1</code>,<code>p2</code>指向空间的值. 继续遍历, 直到 <code>p1=p2</code> , 停止折磨.</li>
<li>考察指针停止的位置, 如果该位置比原基准值大, 则要于基准值交换. 反之, 下一次处理的序列将要改变 : 即基准值变为该指针后面最近的一个值. (这一部分比较难以理解, 目的是为了防止指针停止位置的值没有被考察而产生错误后果.)</li>
<li>取基准值左右两部分序列, 重复上述操作. </li>
</ol>
<h4 id="代码实现-2"><a href="#代码实现-2" class="headerlink" title="代码实现"></a>代码实现</h4><p>快速排序非常重要, 这里代码的实现给出两种:</p>
<h5 id="递归实现"><a href="#递归实现" class="headerlink" title="递归实现"></a>递归实现</h5><p>递归实现比较易于完成, 但是递归所产生的调用栈也要算作算法本身的使用空间, 这使得算法徒增空间复杂度.</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">QuickSort</span> </span>&#123;</span><br><span class="line">    <span class="comment">// 这里仅仅是一个数组指针, 没有引入过多额外的非常数空间</span></span><br><span class="line">    <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span>[] tmpArr;</span><br><span class="line">    <span class="comment">// 辅助交换函数</span></span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span> x, <span class="keyword">int</span> y)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> tmp;</span><br><span class="line">        tmp = tmpArr[x];</span><br><span class="line">        tmpArr[x] = tmpArr[y];</span><br><span class="line">        tmpArr[y] = tmp;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 核心步骤 递归函数</span></span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sortRecursive</span><span class="params">(<span class="keyword">int</span> start, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">if</span>(start &gt;= end) <span class="keyword">return</span>;</span><br><span class="line">        <span class="comment">// (1) 选取基准</span></span><br><span class="line">        <span class="keyword">int</span> mid = tmpArr[end];</span><br><span class="line">        <span class="comment">// (2.1) 声明左右指针</span></span><br><span class="line">        <span class="keyword">int</span> left = start, right = end-<span class="number">1</span>;</span><br><span class="line">        <span class="keyword">while</span> (left &lt; right) &#123;</span><br><span class="line">            <span class="comment">// (2.2) 指针向中间逼近, 并交换元素</span></span><br><span class="line">            <span class="keyword">while</span> (tmpArr[left] &lt;= mid &amp;&amp; left &lt; right) &#123;</span><br><span class="line">                ++left;</span><br><span class="line">            &#125;</span><br><span class="line">            <span class="keyword">while</span> (tmpArr[right] &gt;= mid &amp;&amp; left &lt; right) &#123;</span><br><span class="line">                --right;</span><br><span class="line">            &#125;</span><br><span class="line">            swap(left, right);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// (3) 考察指针结束位置和基准值, 避免忽略</span></span><br><span class="line">        <span class="keyword">if</span>(tmpArr[left] &gt;= tmpArr[end]) &#123;</span><br><span class="line">            swap(left, end);</span><br><span class="line">        &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">            ++left;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// (4) 递归处理</span></span><br><span class="line">        sortRecursive(start, left-<span class="number">1</span>);</span><br><span class="line">        sortRecursive(left+<span class="number">1</span>, end);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 递归实现</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(<span class="keyword">int</span>[] arr)</span> </span>&#123;</span><br><span class="line">        tmpArr = arr;</span><br><span class="line">        sortRecursive(<span class="number">0</span>, tmpArr.length-<span class="number">1</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h5 id="迭代实现"><a href="#迭代实现" class="headerlink" title="迭代实现"></a>迭代实现</h5><p>尾递归算法通常十分容易改写成迭代算法.<br>一个通常的思路是 : 模拟递归实现时的 <strong>递归栈 帧</strong> .</p>
<p>实现方案比较复杂 :</p>
<ul>
<li>为了实现无依赖, 这里采用了手动实现循环队列的方式.</li>
<li>声明一个范围类, 通过范围类入队出队来确定下一次循环迭代的处理范围.</li>
<li>直到队列为空.</li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 本段代码可封神 (</span></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">QuickSort</span> </span>&#123;</span><br><span class="line">    <span class="comment">// 范围类, 用于确定下一次迭代范围</span></span><br><span class="line">    <span class="keyword">static</span> <span class="class"><span class="keyword">class</span> <span class="title">qsRange</span></span>&#123;</span><br><span class="line">        <span class="keyword">public</span> <span class="keyword">int</span> left;</span><br><span class="line">        <span class="keyword">public</span> <span class="keyword">int</span> right;</span><br><span class="line">        <span class="function"><span class="keyword">public</span> <span class="title">qsRange</span><span class="params">(<span class="keyword">int</span> l, <span class="keyword">int</span> r)</span></span>&#123;</span><br><span class="line">            left = l;</span><br><span class="line">            right = r;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 循环队列模拟器</span></span><br><span class="line">    <span class="keyword">private</span> <span class="keyword">static</span> <span class="class"><span class="keyword">class</span> <span class="title">QueueSimulator</span></span>&#123;</span><br><span class="line">        <span class="keyword">private</span> <span class="keyword">static</span> qsRange[] queRange;</span><br><span class="line">        <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span> quePos, insertPos, queSize, _maxSize;</span><br><span class="line">        <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">init</span><span class="params">(<span class="keyword">int</span> maxSize)</span> </span>&#123;</span><br><span class="line">            queRange = <span class="keyword">new</span> qsRange[maxSize];</span><br><span class="line">            _maxSize = maxSize;</span><br><span class="line">            queSize = quePos = insertPos = <span class="number">0</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">push</span><span class="params">(qsRange range)</span> </span>&#123;</span><br><span class="line">            queRange[insertPos++] = range;</span><br><span class="line">            insertPos %= _maxSize;</span><br><span class="line">            ++queSize;</span><br><span class="line">            <span class="keyword">if</span>(queSize &gt; queRange.length) <span class="keyword">throw</span> <span class="keyword">new</span> Error(<span class="string">&quot;挤爆了....&quot;</span>);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">pop</span><span class="params">()</span> </span>&#123;</span><br><span class="line">            queRange[quePos++] = <span class="keyword">null</span>;</span><br><span class="line">            quePos %= _maxSize;</span><br><span class="line">            --queSize;</span><br><span class="line">            <span class="keyword">if</span>(queSize &lt; <span class="number">0</span>) <span class="keyword">throw</span> <span class="keyword">new</span> Error(<span class="string">&quot;榨干了....&quot;</span>);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">boolean</span> <span class="title">empty</span><span class="params">()</span> </span>&#123;</span><br><span class="line">            <span class="keyword">return</span> queSize==<span class="number">0</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> qsRange <span class="title">front</span><span class="params">()</span> </span>&#123;</span><br><span class="line">            <span class="keyword">return</span> queRange[quePos];</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 主题逻辑部分</span></span><br><span class="line">    <span class="comment">// 临时存储用指针</span></span><br><span class="line">    <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span>[] tmpArr;</span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span> j, <span class="keyword">int</span> k)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">if</span>(j==k) <span class="keyword">return</span>;</span><br><span class="line">        <span class="keyword">int</span> tmp = tmpArr[j];</span><br><span class="line">        tmpArr[j] = tmpArr[k];</span><br><span class="line">        tmpArr[k] = tmp;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 迭代实现</span></span><br><span class="line">    <span class="comment">// 原理和递归实现相同, 只是把尾递归的部分换成入队列</span></span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sortIterative</span><span class="params">(qsRange range)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> pleft = range.left, pright = range.right;</span><br><span class="line">        <span class="keyword">if</span>(pleft &gt;= pright) &#123; <span class="keyword">return</span>; &#125;</span><br><span class="line">        <span class="keyword">if</span>(pright - pleft == <span class="number">1</span>) &#123;</span><br><span class="line">            <span class="keyword">if</span>(tmpArr[pright] &lt; tmpArr[pleft]) &#123;</span><br><span class="line">                swap(pleft, pright);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">int</span> mid = tmpArr[pright];</span><br><span class="line">        <span class="keyword">while</span> (pleft &lt; pright) &#123;</span><br><span class="line">            <span class="keyword">while</span> (tmpArr[pleft]&lt;=mid &amp;&amp; pleft&lt;pright) &#123;</span><br><span class="line">                ++pleft;</span><br><span class="line">            &#125;</span><br><span class="line">            <span class="keyword">while</span> (tmpArr[pright]&gt;=mid &amp;&amp; pleft &lt; pright) &#123;</span><br><span class="line">                --pright;</span><br><span class="line">            &#125;</span><br><span class="line">            swap(pleft, pright);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">if</span>(tmpArr[pleft] &gt;= mid) &#123;</span><br><span class="line">            swap(pleft, range.right);</span><br><span class="line">        &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">            ++pleft;</span><br><span class="line">        &#125;</span><br><span class="line">        QueueSimulator.push(<span class="keyword">new</span> qsRange(range.left, pleft-<span class="number">1</span>));</span><br><span class="line">        QueueSimulator.push(<span class="keyword">new</span> qsRange(pleft+<span class="number">1</span>, range.right));</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 迭代调用</span></span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(<span class="keyword">int</span>[] arr)</span> </span>&#123;</span><br><span class="line">        tmpArr = arr;</span><br><span class="line">        <span class="comment">// 这个位置的队列长度可以使用数学优化, </span></span><br><span class="line">        <span class="comment">// 很显然使用更小的栈或队列可以更好的优化本例, 但是我没算出来 (</span></span><br><span class="line">        QueueSimulator.init(arr.length/<span class="number">4</span> + <span class="number">16</span>);</span><br><span class="line">        QueueSimulator.push(<span class="keyword">new</span> qsRange(<span class="number">0</span>, arr.length-<span class="number">1</span>));</span><br><span class="line">        <span class="keyword">while</span>(!QueueSimulator.empty()) &#123;</span><br><span class="line">            sortIterative(QueueSimulator.front());</span><br><span class="line">            QueueSimulator.pop();</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>


<h4 id="实用分析-2"><a href="#实用分析-2" class="headerlink" title="实用分析"></a>实用分析</h4><p>快速排序是最实用的算法. 他能够适应几乎任何情况的排序(例如字符串的字典序, 可以通过重写比较函数来实现), 而且时空复杂度都是极底的(不是最低). </p>
<p>缺点在于快排不是稳定的算法, 过多次数的交换操作导致了他的不稳定性. </p>
<hr>
<h3 id="堆排序-HeapSort"><a href="#堆排序-HeapSort" class="headerlink" title="堆排序 HeapSort"></a>堆排序 HeapSort</h3><h4 id="原理-3"><a href="#原理-3" class="headerlink" title="原理"></a>原理</h4><p>堆排序并不需要完整的构建一个堆, 而是恰当的使用构建堆的原理. </p>
<h5 id="恰当使用位运算"><a href="#恰当使用位运算" class="headerlink" title="恰当使用位运算"></a>恰当使用位运算</h5><p>当我们构建一个完全二叉树时, 考察顺序构建时<code>[索引号+1](二进制)</code>的情况, 会出现神奇的效果 : </p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line">                          1</span><br><span class="line">                    &#x2F;           \</span><br><span class="line">            10                         11</span><br><span class="line">        &#x2F;       \                  &#x2F;        \</span><br><span class="line">   100           101           110           111</span><br><span class="line">   &#x2F;  \         &#x2F;    \        &#x2F;    \        &#x2F;    \</span><br><span class="line">1000  1001    1010  1011    1100  1101    1110  1111</span><br></pre></td></tr></table></figure>

<p>也就意味着, 基于这一点, 我们可以通过位运算来直接找到每个值的索引位置.</p>
<blockquote>
<p>这里使用 <code>[索引-1]</code> 的方式也能获得类似的效果, 自然在实现细节上需要做相应调整</p>
</blockquote>
<h5 id="堆的调整"><a href="#堆的调整" class="headerlink" title="堆的调整"></a>堆的调整</h5><p>以大顶堆为例, 堆的调整方法为向下调整 :</p>
<ol>
<li>如果该节点的叶节点中, 较大者大于他, 则该节点与该叶节点交换</li>
<li>如果交换了, 则继续向下调整被换掉的叶节点</li>
</ol>
<p>我们构建堆时, 首先即需要基于原序列构建无序堆, 随即对所有的第一个非叶节点进行向上调整, 即可完成建堆</p>
<h5 id="最终整合"><a href="#最终整合" class="headerlink" title="最终整合"></a>最终整合</h5><p>整理知识点, 理清算法 :</p>
<ol>
<li>通过序列构建无序堆.</li>
<li>向下调整, 将无序堆有序化.</li>
<li>依次从后至前遍历序列, 每次将该节点和堆顶交换, 并完成向下调整, 注意不要换掉已经整体交换过的元素.</li>
</ol>
<h4 id="代码实现-3"><a href="#代码实现-3" class="headerlink" title="代码实现"></a>代码实现</h4><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">HeapSort</span> </span>&#123;</span><br><span class="line">    <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span>[] tmpArr;</span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span> i, <span class="keyword">int</span> j)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> tmp = tmpArr[i];</span><br><span class="line">        tmpArr[i] = tmpArr[j];</span><br><span class="line">        tmpArr[j] = tmp;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 参数为 逻辑坐标, 最大实际节点</span></span><br><span class="line">    <span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">adjust</span><span class="params">(<span class="keyword">int</span> index, <span class="keyword">int</span> len)</span> </span>&#123;</span><br><span class="line">        <span class="comment">// 左右节点的逻辑坐标</span></span><br><span class="line">        <span class="keyword">int</span> left = index*<span class="number">2</span>, right = left+<span class="number">1</span>;</span><br><span class="line">        <span class="comment">// 记录最大点 逻辑坐标</span></span><br><span class="line">        <span class="keyword">int</span> pMax = left;</span><br><span class="line">        <span class="comment">// 左节点判空</span></span><br><span class="line">        <span class="keyword">if</span> (left-<span class="number">1</span> &gt; len) <span class="keyword">return</span>;</span><br><span class="line">        <span class="comment">// 右节点判空, 并判断左右子树</span></span><br><span class="line">        <span class="keyword">if</span> (right-<span class="number">1</span>&lt;=len &amp;&amp; tmpArr[right-<span class="number">1</span>] &gt; tmpArr[left-<span class="number">1</span>]) &#123;</span><br><span class="line">            pMax = right;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// 判断调整</span></span><br><span class="line">        <span class="keyword">if</span> (tmpArr[index-<span class="number">1</span>] &lt; tmpArr[pMax-<span class="number">1</span>]) &#123;</span><br><span class="line">            swap(index-<span class="number">1</span>, pMax-<span class="number">1</span>);</span><br><span class="line">            adjust(pMax, len);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(<span class="keyword">int</span>[] arr)</span> </span>&#123;</span><br><span class="line">        <span class="comment">// 建堆</span></span><br><span class="line">        tmpArr = arr;</span><br><span class="line">        <span class="keyword">int</span> len = tmpArr.length - <span class="number">1</span>;</span><br><span class="line">        <span class="comment">// 枚举叶子节点, 向下调整初始化堆</span></span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=len/<span class="number">2</span>+<span class="number">2</span>; i&gt;=<span class="number">1</span>; --i) &#123;</span><br><span class="line">            adjust(i, len);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="comment">// 排序</span></span><br><span class="line">        <span class="keyword">for</span>(<span class="keyword">int</span> i=len; i&gt;=<span class="number">1</span>; --i) &#123;</span><br><span class="line">            swap(<span class="number">0</span>, i);</span><br><span class="line">            adjust(<span class="number">1</span>, i-<span class="number">1</span>);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h4 id="实用分析-3"><a href="#实用分析-3" class="headerlink" title="实用分析"></a>实用分析</h4><p>堆排序不常用, 但是堆这种数据结构十分常见. 可以用于实现优先权队列, 构建哈夫曼树等等. 在操作系统中也有丰富的应用.</p>
<p>~~手写堆排序主要是为了练习堆这种数据结构. ~~</p>

    </div>

    
    
    
        <div class="reward-container">
  <div></div>
  <button onclick="var qr = document.getElementById('qr'); qr.style.display = (qr.style.display === 'none') ? 'block' : 'none';">
    打赏
  </button>
  <div id="qr" style="display: none;">
      
      <div style="display: inline-block;">
        <img src="/images/wechatpay.png" alt="Hanamaru🍥Yabuki 微信支付">
        <p>微信支付</p>
      </div>
      
      <div style="display: inline-block;">
        <img src="/images/alipay.png" alt="Hanamaru🍥Yabuki 支付宝">
        <p>支付宝</p>
      </div>

  </div>
</div>


      <footer class="post-footer">
          
          <div class="post-tags">
              <a href="/tags/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95/" rel="tag"><i class="fa fa-tag"></i> 排序算法</a>
              <a href="/tags/Java/" rel="tag"><i class="fa fa-tag"></i> Java</a>
          </div>

        


        
    <div class="post-nav">
      <div class="post-nav-item">
    <a href="/2020/11/29/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E7%BB%93-%E4%B8%80/" rel="prev" title="排序算法总结(一)">
      <i class="fa fa-chevron-left"></i> 排序算法总结(一)
    </a></div>
      <div class="post-nav-item">
    <a href="/2020/11/30/%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E7%BB%93-%E4%B8%89/" rel="next" title="排序算法总结(三)">
      排序算法总结(三) <i class="fa fa-chevron-right"></i>
    </a></div>
    </div>
      </footer>
    
  </article>
  
  
  



          </div>
          

<script>
  window.addEventListener('tabs:register', () => {
    let { activeClass } = CONFIG.comments;
    if (CONFIG.comments.storage) {
      activeClass = localStorage.getItem('comments_active') || activeClass;
    }
    if (activeClass) {
      let activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
      if (activeTab) {
        activeTab.click();
      }
    }
  });
  if (CONFIG.comments.storage) {
    window.addEventListener('tabs:click', event => {
      if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
      let commentClass = event.target.classList[1];
      localStorage.setItem('comments_active', commentClass);
    });
  }
</script>

        </div>
          
  
  <div class="toggle sidebar-toggle">
    <span class="toggle-line toggle-line-first"></span>
    <span class="toggle-line toggle-line-middle"></span>
    <span class="toggle-line toggle-line-last"></span>
  </div>

  <aside class="sidebar">
    <div class="sidebar-inner">

      <ul class="sidebar-nav motion-element">
        <li class="sidebar-nav-toc">
          文章目录
        </li>
        <li class="sidebar-nav-overview">
          站点概览
        </li>
      </ul>

      <!--noindex-->
      <div class="post-toc-wrap sidebar-panel">
          <div class="post-toc motion-element"><ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E7%BB%93-%E4%BA%8C-%E6%91%98%E8%A6%81"><span class="nav-number">1.</span> <span class="nav-text">排序算法总结(二) - 摘要</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E7%85%A7%E4%BE%8B%E5%85%88%E6%9D%A5-%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%80%BB%E8%A7%88"><span class="nav-number">2.</span> <span class="nav-text">照例先来 排序算法总览</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%BD%92%E5%B9%B6%E6%8E%92%E5%BA%8F-MergeSort"><span class="nav-number">2.1.</span> <span class="nav-text">归并排序 MergeSort</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%8E%9F%E7%90%86"><span class="nav-number">2.1.1.</span> <span class="nav-text">原理</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0"><span class="nav-number">2.1.2.</span> <span class="nav-text">代码实现</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9E%E7%94%A8%E5%88%86%E6%9E%90"><span class="nav-number">2.1.3.</span> <span class="nav-text">实用分析</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%B8%8C%E5%B0%94%E6%8E%92%E5%BA%8F-ShellSort"><span class="nav-number">2.2.</span> <span class="nav-text">希尔排序 ShellSort</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%8E%9F%E7%90%86-1"><span class="nav-number">2.2.1.</span> <span class="nav-text">原理</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0-1"><span class="nav-number">2.2.2.</span> <span class="nav-text">代码实现</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9E%E7%94%A8%E5%88%86%E6%9E%90-1"><span class="nav-number">2.2.3.</span> <span class="nav-text">实用分析</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%BF%AB%E9%80%9F%E6%8E%92%E5%BA%8F-QuickSort"><span class="nav-number">2.3.</span> <span class="nav-text">快速排序 QuickSort</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%8E%9F%E7%90%86-2"><span class="nav-number">2.3.1.</span> <span class="nav-text">原理</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0-2"><span class="nav-number">2.3.2.</span> <span class="nav-text">代码实现</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0"><span class="nav-number">2.3.2.1.</span> <span class="nav-text">递归实现</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E8%BF%AD%E4%BB%A3%E5%AE%9E%E7%8E%B0"><span class="nav-number">2.3.2.2.</span> <span class="nav-text">迭代实现</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9E%E7%94%A8%E5%88%86%E6%9E%90-2"><span class="nav-number">2.3.3.</span> <span class="nav-text">实用分析</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%A0%86%E6%8E%92%E5%BA%8F-HeapSort"><span class="nav-number">2.4.</span> <span class="nav-text">堆排序 HeapSort</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%8E%9F%E7%90%86-3"><span class="nav-number">2.4.1.</span> <span class="nav-text">原理</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%81%B0%E5%BD%93%E4%BD%BF%E7%94%A8%E4%BD%8D%E8%BF%90%E7%AE%97"><span class="nav-number">2.4.1.1.</span> <span class="nav-text">恰当使用位运算</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%A0%86%E7%9A%84%E8%B0%83%E6%95%B4"><span class="nav-number">2.4.1.2.</span> <span class="nav-text">堆的调整</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%9C%80%E7%BB%88%E6%95%B4%E5%90%88"><span class="nav-number">2.4.1.3.</span> <span class="nav-text">最终整合</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0-3"><span class="nav-number">2.4.2.</span> <span class="nav-text">代码实现</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9E%E7%94%A8%E5%88%86%E6%9E%90-3"><span class="nav-number">2.4.3.</span> <span class="nav-text">实用分析</span></a></li></ol></li></ol></li></ol></div>
      </div>
      <!--/noindex-->

      <div class="site-overview-wrap sidebar-panel">
        <div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person">
    <img class="site-author-image" itemprop="image" alt="Hanamaru🍥Yabuki"
      src="/images/avatar.gif">
  <p class="site-author-name" itemprop="name">Hanamaru🍥Yabuki</p>
  <div class="site-description" itemprop="description"></div>
</div>
<div class="site-state-wrap motion-element">
  <nav class="site-state">
      <div class="site-state-item site-state-posts">
          <a href="/archives/">
        
          <span class="site-state-item-count">13</span>
          <span class="site-state-item-name">日志</span>
        </a>
      </div>
      <div class="site-state-item site-state-categories">
            <a href="/categories/">
          
        <span class="site-state-item-count">5</span>
        <span class="site-state-item-name">分类</span></a>
      </div>
      <div class="site-state-item site-state-tags">
            <a href="/tags/">
          
        <span class="site-state-item-count">7</span>
        <span class="site-state-item-name">标签</span></a>
      </div>
  </nav>
</div>
  <div class="links-of-author motion-element">
      <span class="links-of-author-item">
        <a href="https://github.com/HanaYabuki" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;HanaYabuki" rel="noopener" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
      </span>
      <span class="links-of-author-item">
        <a href="https://space.bilibili.com/496956009" title="Bilibili → https:&#x2F;&#x2F;space.bilibili.com&#x2F;496956009" rel="noopener" target="_blank"><i class="fab fa-youtube fa-fw"></i>Bilibili</a>
      </span>
  </div>



      </div>

    </div>
  </aside>
  <div id="sidebar-dimmer"></div>


      </div>
    </main>

    <footer class="footer">
      <div class="footer-inner">
        

        

<div class="copyright">
  
  &copy; 
  <span itemprop="copyrightYear">2021</span>
  <span class="with-love">
    <i class="fa fa-heart"></i>
  </span>
  <span class="author" itemprop="copyrightHolder">Hanamaru🍥Yabuki</span>
</div>
  <div class="powered-by">由 <a href="https://hexo.io/" class="theme-link" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.org/" class="theme-link" rel="noopener" target="_blank">NexT.Gemini</a> 强力驱动
  </div>

        








      </div>
    </footer>
  </div>

  
  <script src="/lib/anime.min.js"></script>
  <script src="//cdn.jsdelivr.net/npm/lozad@1/dist/lozad.min.js"></script>
  <script src="/lib/velocity/velocity.min.js"></script>
  <script src="/lib/velocity/velocity.ui.min.js"></script>

<script src="/js/utils.js"></script>

<script src="/js/motion.js"></script>


<script src="/js/schemes/pisces.js"></script>


<script src="/js/next-boot.js"></script>




  
  <script>
    (function(){
      var canonicalURL, curProtocol;
      //Get the <link> tag
      var x=document.getElementsByTagName("link");
		//Find the last canonical URL
		if(x.length > 0){
			for (i=0;i<x.length;i++){
				if(x[i].rel.toLowerCase() == 'canonical' && x[i].href){
					canonicalURL=x[i].href;
				}
			}
		}
    //Get protocol
	    if (!canonicalURL){
	    	curProtocol = window.location.protocol.split(':')[0];
	    }
	    else{
	    	curProtocol = canonicalURL.split(':')[0];
	    }
      //Get current URL if the canonical URL does not exist
	    if (!canonicalURL) canonicalURL = window.location.href;
	    //Assign script content. Replace current URL with the canonical URL
      !function(){var e=/([http|https]:\/\/[a-zA-Z0-9\_\.]+\.baidu\.com)/gi,r=canonicalURL,t=document.referrer;if(!e.test(r)){var n=(String(curProtocol).toLowerCase() === 'https')?"https://sp0.baidu.com/9_Q4simg2RQJ8t7jm9iCKT-xh_/s.gif":"//api.share.baidu.com/s.gif";t?(n+="?r="+encodeURIComponent(document.referrer),r&&(n+="&l="+r)):r&&(n+="?l="+r);var i=new Image;i.src=n}}(window);})();
  </script>















  

  

</body>
</html>
